This article includes a list of general references, but it lacks sufficient corresponding inline citations .(March 2013) |
An inquiry (also spelled as enquiry in British English) [lower-alpha 1] is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.
When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By 'middle term' I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by 'extremes' (a) that which is contained in another, and (b) that in which another is contained. For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C. ... I call this kind of figure the First. (Aristotle, Prior Analytics, 1.4)
Inductive reasoning consists in establishing a relation between one extreme term and the middle term by means of the other extreme; for example, if B is the middle term of A and C, in proving by means of C that A applies to B; for this is how we effect inductions. (Aristotle, Prior Analytics, 2.23)
The locus classicus for the study of abductive reasoning is found in Aristotle's Prior Analytics , Book 2, Chapt. 25. It begins this way:
We have Reduction (απαγωγη, abduction):
- When it is obvious that the first term applies to the middle, but that the middle applies to the last term is not obvious, yet is nevertheless more probable or not less probable than the conclusion;
- Or if there are not many intermediate terms between the last and the middle;
For in all such cases the effect is to bring us nearer to knowledge.
By way of explanation, Aristotle supplies two very instructive examples, one for each of the two varieties of abductive inference steps that he has just described in the abstract:
- For example, let A stand for "that which can be taught", B for "knowledge", and C for "morality". Then that knowledge can be taught is evident; but whether virtue is knowledge is not clear. Then if BC is not less probable or is more probable than AC, we have reduction; for we are nearer to knowledge for having introduced an additional term, whereas before we had no knowledge that AC is true.
- Or again we have reduction if there are not many intermediate terms between B and C; for in this case too we are brought nearer to knowledge. For example, suppose that D is "to square", E "rectilinear figure", and F "circle". Assuming that between E and F there is only one intermediate term — that the circle becomes equal to a rectilinear figure by means of lunules — we should approximate to knowledge. (Aristotle, "Prior Analytics", 2.25, with minor alterations)
Aristotle's latter variety of abductive reasoning, though it will take some explaining in the sequel, is well worth our contemplation, since it hints already at streams of inquiry that course well beyond the syllogistic source from which they spring, and into regions that Peirce will explore more broadly and deeply.
In the pragmatic philosophies of Charles Sanders Peirce, William James, John Dewey, and others, inquiry is closely associated with the normative science of logic. In its inception, the pragmatic model or theory of inquiry was extracted by Peirce from its raw materials in classical logic, with a little bit of help from Kant, and refined in parallel with the early development of symbolic logic by Boole, De Morgan, and Peirce himself to address problems about the nature and conduct of scientific reasoning. Borrowing a brace of concepts from Aristotle, Peirce examined three fundamental modes of reasoning that play a role in inquiry, commonly known as abductive, deductive, and inductive inference.
In rough terms, abduction is what we use to generate a likely hypothesis or an initial diagnosis in response to a phenomenon of interest or a problem of concern, while deduction is used to clarify, to derive, and to explicate the relevant consequences of the selected hypothesis, and induction is used to test the sum of the predictions against the sum of the data. It needs to be observed that the classical and pragmatic treatments of the types of reasoning, dividing the generic territory of inference as they do into three special parts, arrive at a different characterization of the environs of reason than do those accounts that count only two.
These three processes typically operate in a cyclic fashion, systematically operating to reduce the uncertainties and the difficulties that initiated the inquiry in question, and in this way, to the extent that inquiry is successful, leading to an increase in knowledge or in skills.
In the pragmatic way of thinking everything has a purpose, and the purpose of each thing is the first thing we should try to note about it. [2] The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call knowledge or certainty . As they contribute to the end of inquiry, we should appreciate that the three kinds of inference describe a cycle that can be understood only as a whole, and none of the three makes complete sense in isolation from the others. For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and that induction can evaluate. This places a mild but meaningful constraint on the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality. In a similar fashion, each of the other types of inference realizes its purpose only in accord with its proper role in the whole cycle of inquiry. No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its principal components.
In Logic: The Theory of Inquiry, John Dewey defined inquiry as "the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole". [3] Dewey and Peirce's conception of inquiry extended beyond a system of thinking and incorporated the social nature of inquiry. These ideas are summarize in the notion Community of inquiry. [4] [5] [6]
This section is written like a personal reflection, personal essay, or argumentative essay that states a Wikipedia editor's personal feelings or presents an original argument about a topic.(May 2024) |
For our present purposes, the first feature to note in distinguishing the three principal modes of reasoning from each other is whether each of them is exact or approximate in character. In this light, deduction is the only one of the three types of reasoning that can be made exact, in essence, always deriving true conclusions from true premises, while abduction and induction are unavoidably approximate in their modes of operation, involving elements of fallible judgment in practice and inescapable error in their application.
The reason for this is that deduction, in the ideal limit, can be rendered a purely internal process of the reasoning agent, while the other two modes of reasoning essentially demand a constant interaction with the outside world, a source of phenomena and problems that will no doubt continue to exceed the capacities of any finite resource, human or machine, to master. Situated in this larger reality, approximations can be judged appropriate only in relation to their context of use and can be judged fitting only with regard to a purpose in view.
A parallel distinction that is often made in this connection is to call deduction a demonstrative form of inference, while abduction and induction are classed as non-demonstrative forms of reasoning. Strictly speaking, the latter two modes of reasoning are not properly called inferences at all. They are more like controlled associations of words or ideas that just happen to be successful often enough to be preserved as useful heuristic strategies in the repertoire of the agent. But non-demonstrative ways of thinking are inherently subject to error, and must be constantly checked out and corrected as needed in practice.
In classical terminology, forms of judgment that require attention to the context and the purpose of the judgment are said to involve an element of "art", in a sense that is judged to distinguish them from "science", and in their renderings as expressive judgments to implicate arbiters in styles of rhetoric, as contrasted with logic.
In a figurative sense, this means that only deductive logic can be reduced to an exact theoretical science, while the practice of any empirical science will always remain to some degree an art.
C. S. Peirce argued that inquiry reaches a logical limit, or "approximate[s] indefinitely toward that limit", which he regarded as "truth". [7]
Jewish rabbinical writers used the text of Deuteronomy 4:32 in the Hebrew Bible, or ask now concerning the days that are past, which were before you, since the day that God created man on the earth, and ask from one end of heaven to the other, whether any great thing like this has happened, or anything like it has been heard, [8] to impose ethical limits on inquiry, forbidding inquiry into the work of creation in the presence of two people, reading the words "for ask now of the days past" to indicate that one may inquire, but not two. The Rabbis reasoned that the words "since the day that God created man upon the earth" in this verse taught that one must not inquire concerning the time before creation, but that the words "the days past that were before you" meant that one may inquire about the six days of creation. They further reasoned that the words "from the one end of heaven to the other" indicated that one must not inquire about what is beyond the universe, what is above and what is below, what is before and what is after. [9]
Many aspects of inquiry can be recognized and usefully studied in very basic logical settings, even simpler than the level of syllogism, for example, in the realm of reasoning that is variously known as Boolean algebra , propositional calculus , sentential calculus, or zeroth-order logic. By way of approaching the learning curve on the gentlest availing slope, we may well begin at the level of zeroth-order inquiry , in effect, taking the syllogistic approach to inquiry only so far as the propositional or sentential aspects of the associated reasoning processes are concerned. One of the bonuses of doing this in the context of Peirce's logical work is that it provides us with doubly instructive exercises in the use of his logical graphs, taken at the level of his so-called "alpha graphs".
In the case of propositional calculus or sentential logic, deduction comes down to applications of the transitive law for conditional implications and the approximate forms of inference hang on the properties that derive from these. In describing the various types of inference I will employ a few old "terms of art" from classical logic that are still of use in treating these kinds of simple problems in reasoning.
For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them.
o-------------------------------------------------o | | | Z | | o | | |\ | | | \ | | | \ | | | \ | | | \ | | | \ R U L E | | | \ | | | \ | | F | \ | | | \ | | A | \ | | | o Y | | C | / | | | / | | T | / | | | / | | | / | | | / C A S E | | | / | | | / | | | / | | | / | | |/ | | o | | X | | | | Deduction takes a Case of the form X → Y, | | matches it with a Rule of the form Y → Z, | | then adverts to a Fact of the form X → Z. | | | | Induction takes a Case of the form X → Y, | | matches it with a Fact of the form X → Z, | | then adverts to a Rule of the form Y → Z. | | | | Abduction takes a Fact of the form X → Z, | | matches it with a Rule of the form Y → Z, | | then adverts to a Case of the form X → Y. | | | | Even more succinctly: | | | | Abduction Deduction Induction | | | | Premise: Fact Case Case | | Premise: Rule Rule Fact | | Outcome: Case Fact Rule | | | o-------------------------------------------------o Figure 1. Elementary Structure and Terminology |
In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence. In contrast, a statement of Case may refer to a hidden or a hypothetical cause, that is, a type of event that is not immediately observable to all concerned. Obviously, the distinction is a rough one and the question of which mode applies can depend on the points of view that different observers adopt over time. Finally, a statement of a Rule is called that because it states a regularity or a regulation that governs a whole class of situations, and not because of its syntactic form. So far in this discussion, all three types of constraint are expressed in the form of conditional propositions, but this is not a fixed requirement. In practice, these modes of statement are distinguished by the roles that they play within an argument, not by their style of expression. When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.
Examples of inquiry, that illustrate the full cycle of its abductive, deductive, and inductive phases, and yet are both concrete and simple enough to be suitable for a first (or zeroth) exposition, are somewhat rare in Peirce's writings, and so let us draw one from the work of fellow pragmatician John Dewey, analyzing it according to the model of zeroth-order inquiry that we developed above.
A man is walking on a warm day. The sky was clear the last time he observed it; but presently he notes, while occupied primarily with other things, that the air is cooler. It occurs to him that it is probably going to rain; looking up, he sees a dark cloud between him and the sun, and he then quickens his steps. What, if anything, in such a situation can be called thought? Neither the act of walking nor the noting of the cold is a thought. Walking is one direction of activity; looking and noting are other modes of activity. The likelihood that it will rain is, however, something suggested. The pedestrian feels the cold; he thinks of clouds and a coming shower. (John Dewey, How We Think , 1910, pp. 6-7).
Let's first give Dewey's example of inquiry in everyday life the quick once over, hitting just the high points of its analysis into Peirce's three kinds of reasoning.
In Dewey's "Rainy Day" or "Sign of Rain" story, we find our peripatetic hero presented with a surprising Fact:
Responding to an intellectual reflex of puzzlement about the situation, his resource of common knowledge about the world is impelled to seize on an approximate Rule:
This Rule can be recognized as having a potential relevance to the situation because it matches the surprising Fact, C → A, in its consequential feature A.
All of this suggests that the present Case may be one in which it is just about to rain:
The whole mental performance, however automatic and semi-conscious it may be, that leads up from a problematic Fact and a previously settled knowledge base of Rules to the plausible suggestion of a Case description, is what we are calling an abductive inference.
The next phase of inquiry uses deductive inference to expand the implied consequences of the abductive hypothesis, with the aim of testing its truth. For this purpose, the inquirer needs to think of other things that would follow from the consequence of his precipitate explanation. Thus, he now reflects on the Case just assumed:
He looks up to scan the sky, perhaps in a random search for further information, but since the sky is a logical place to look for details of an imminent rainstorm, symbolized in our story by the letter B, we may safely suppose that our reasoner has already detached the consequence of the abduced Case, C → B, and has begun to expand on its further implications. So let us imagine that our up-looker has a more deliberate purpose in mind, and that his search for additional data is driven by the new-found, determinate Rule:
Contemplating the assumed Case in combination with this new Rule leads him by an immediate deduction to predict an additional Fact:
The reconstructed picture of reasoning assembled in this second phase of inquiry is true to the pattern of deductive inference.
Whatever the case, our subject observes a Dark cloud, just as he would expect on the basis of the new hypothesis. The explanation of imminent rain removes the discrepancy between observations and expectations and thereby reduces the shock of surprise that made this process of inquiry necessary.
Figure 4 gives a graphical illustration of Dewey's example of inquiry, isolating for the purposes of the present analysis the first two steps in the more extended proceedings that go to make up the whole inquiry.
o-----------------------------------------------------------o | | | A D | | o o | | \ * * / | | \ * * / | | \ * * / | | \ * * / | | \ * * / | | \ R u l e R u l e / | | \ * * / | | \ * * / | | \ * * / | | \ * B * / | | F a c t o F a c t | | \ * / | | \ * / | | \ * / | | \ * / | | \ C a s e / | | \ * / | | \ * / | | \ * / | | \ * / | | \ * / | | \*/ | | o | | C | | | | A = the Air is cool | | B = just Before it rains | | C = the Current situation | | D = a Dark cloud appears | | | | A is a major term | | B is a middle term | | C is a minor term | | D is a major term, associated with A | | | o-----------------------------------------------------------o Figure 4. Dewey's 'Rainy Day' Inquiry
In this analysis of the first steps of Inquiry, we have a complex or a mixed form of inference that can be seen as taking place in two steps:
This is nowhere near a complete analysis of the Rainy Day inquiry, even insofar as it might be carried out within the constraints of the syllogistic framework, and it covers only the first two steps of the relevant inquiry process, but maybe it will do for a start.
One other thing needs to be noticed here, the formal duality between this expansion phase of inquiry and the argument from analogy. This can be seen most clearly in the propositional lattice diagrams shown in Figures 3 and 4, where analogy exhibits a rough "A" shape and the first two steps of inquiry exhibit a rough "V" shape, respectively. Since we find ourselves repeatedly referring to this expansion phase of inquiry as a unit, let's give it a name that suggests its duality with analogy—"catalogy" will do for the moment. This usage is apt enough if one thinks of a catalogue entry for an item as a text that lists its salient features. Notice that analogy has to do with the examples of a given quality, while catalogy has to do with the qualities of a given example. Peirce noted similar forms of duality in many of his early writings, leading to the consummate treatment in his 1867 paper "On a New List of Categories" (CP 1.545-559, W 2, 49-59).
In order to comprehend the bearing of inductive reasoning on the closing phases of inquiry there are a couple of observations that we need to make:
Throughout inquiry the reasoner makes use of rules that have to be transported across intervals of experience, from the masses of experience where they are learned to the moments of experience where they are applied. Inductive reasoning is involved in the learning and the transfer of these rules, both in accumulating a knowledge base and in carrying it through the times between acquisition and application.
Let's now consider how these principles of learning, transfer, and testing apply to John Dewey's "Sign of Rain" example.
Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference.
For example, a rule like:
is usually induced from a consideration of many past events, in a manner that can be rationally reconstructed as follows:
However, the very same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a presumptive theory.
What is it that gives a distinctively inductive character to the acquisition of a knowledge base? It is evidently the "analogy of experience" that underlies its useful application. Whenever we find ourselves prefacing an argument with the phrase "If past experience is any guide..." then we can be sure that this principle has come into play. We are invoking an analogy between past experience, considered as a totality, and present experience, considered as a point of application. What we mean in practice is this: "If past experience is a fair sample of possible experience, then the knowledge gained in it applies to present experience". This is the mechanism that allows a knowledge base to be carried across gulfs of experience that are indifferent to the effective contents of its rules.
Here are the details of how this notion of transfer works out in the case of the "Sign of Rain" example:
Let K(pres) be a portion of the reasoner's knowledge base that is logically equivalent to the conjunction of two rules, as follows:
K(pres) is the present knowledge base, expressed in the form of a logical constraint on the present universe of discourse.
It is convenient to have the option of expressing all logical statements in terms of their logical models, that is, in terms of the primitive circumstances or the elements of experience over which they hold true.
If we think of the knowledge base K(pres) as referring to the "regime of experience" over which it is valid, then all of these sets of models can be compared by the simple relations of set inclusion or logical implication.
Figure 5 schematizes this way of viewing the "analogy of experience".
o-----------------------------------------------------------o | | | K(pres) | | o | | /|\ | | / | \ | | / | \ | | / | \ | | / Rule \ | | / | \ | | / | \ | | / | \ | | / E(poss) \ | | Fact / o \ Fact | | / * * \ | | / * * \ | | / * * \ | | / * * \ | | / * * \ | | / * Case Case * \ | | / * * \ | | / * * \ | | /* *\ | | o<<<---------------<<<---------------<<<o | | E(past) Analogy Morphism E(pres) | | More Known Less Known | | | o-----------------------------------------------------------o Figure 5. Analogy of Experience
In these terms, the "analogy of experience" proceeds by inducing a Rule about the validity of a current knowledge base and then deducing a Fact, its applicability to a current experience, as in the following sequence:
Inductive Phase:
Deductive Phase:
If the observer looks up and does not see dark clouds, or if he runs for shelter but it does not rain, then there is fresh occasion to question the utility or the validity of his knowledge base. But we must leave our foulweather friend for now and defer the logical analysis of this testing phase to another occasion.
Charles Sanders Peirce was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss, Peirce was "the most original and versatile of America's philosophers and America's greatest logician". Bertrand Russell wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever".
In philosophy, empiricism is an epistemological view which holds that true knowledge or justification comes only or primarily from sensory experience and empirical evidence. It is one of several competing views within epistemology, along with rationalism and skepticism. Empiricists argue that empiricism is a more reliable method of finding the truth than purely using logical reasoning, because humans have cognitive biases and limitations which lead to errors of judgement. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. Empiricists may argue that traditions arise due to relations of previous sensory experiences.
Reason is the capacity of applying logic consciously by drawing conclusions from new or existing information, with the aim of seeking the truth. It is associated with such characteristically human activities as philosophy, religion, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans. Reason is sometimes referred to as rationality.
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
Abductive reasoning is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher and logician Charles Sanders Peirce beginning in the latter half of the 19th century.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. This article is concerned with the inductive reasoning other than deductive reasoning, where the conclusion of a deductive argument is certain given the premises are correct; in contrast, the truth of the conclusion of an inductive argument is at best probable, based upon the evidence given.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case. Together, they form an argument. Logical reasoning is norm-governed in the sense that it aims to formulate correct arguments that any rational person would find convincing. The main discipline studying logical reasoning is logic.
"Natural kind" is an intellectual grouping, or categorizing of things, in a manner that is reflective of the actual world and not just human interests. Some treat it as a classification identifying some structure of truth and reality that exists whether or not humans recognize it. Others treat it as intrinsically useful to the human mind, but not necessarily reflective of something more objective. Candidate examples of natural kinds are found in all the sciences, but the field of chemistry provides the paradigm example of elements.
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically. Although automated reasoning is considered a sub-field of artificial intelligence, it also has connections with theoretical computer science and philosophy.
The history of scientific method considers changes in the methodology of scientific inquiry, as distinct from the history of science itself. The development of rules for scientific reasoning has not been straightforward; scientific method has been the subject of intense and recurring debate throughout the history of science, and eminent natural philosophers and scientists have argued for the primacy of one or another approach to establishing scientific knowledge.
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal systemic. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.
Models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge. The philosopher Wesley C. Salmon described scientific inquiry:
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world.
Probabilistic logic involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as in case of belief fusion in Dempster–Shafer theory. Source trust and epistemic uncertainty about the probabilities they provide, such as defined in subjective logic, are additional elements to consider. The need to deal with a broad variety of contexts and issues has led to many different proposals.
Inductivism is the traditional and still commonplace philosophy of scientific method to develop scientific theories. Inductivism aims to neutrally observe a domain, infer laws from examined cases—hence, inductive reasoning—and thus objectively discover the sole naturally true theory of the observed.
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.
The psychology of reasoning is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory.
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", while they are rational according to the broader requirement that they are based on reason and knowledge.